Twisted commutators and internal crossed modules

B. S. Deval and T. Van der Linden

We introduce a notion of relative commutator - an important special case being commutators twisted by an action - as a straightforward modification of the definition of the Higgins commutator, establish its relation with a new notion of commutativity - also obtained as a modification of the usual notion - and show how we can use it to characterise internal crossed modules in the context of a semi-abelian category. 

Advanced Studies: Euro-Tbilisi Mathematical Journal, Vol. 17(3) (2024), pp. 25-52